A) 6 square units
B) 5 square units
C) 4 square units
D) 3 square units
Correct Answer: D
Solution :
[d] Area of \[\Delta \,ABC=\frac{1}{2}\left( \overrightarrow{AB}\times \overrightarrow{AC} \right)\] \[=\frac{1}{2}\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ -2 & 3 & 2 \\ -4 & 5 & 2 \\ \end{matrix} \right|\] \[=\frac{1}{2}\left[ \hat{i}(6-10)-\hat{j}(-4+8)+\hat{k}(-10+12) \right]\] \[=\frac{1}{2}\left[ -4\hat{i}-4\hat{j}+2\hat{k} \right]\] \[=\frac{1}{2}\sqrt{16+16+4}=\frac{1}{2}\sqrt{36}\] \[=\frac{1}{2}\times 6\] \[=3\] square unitsYou need to login to perform this action.
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